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Portions not contributed by visitors are Copyright 2018 Tangient LLC
TES: The largest network of teachers in the world
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These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.
7 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>]
Eigenmonzos: 2, 7/6, 4/3
Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|]
Generators: 2, 6/5, 7
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405
Enlil
Commas: 385/384, 6250/6237Minimax tuning
[|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>,
|3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>]
Eigenmonzos: 2, 4/3, 14/11
Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|]
Generators: 2, 6/5, 7
EDOs: 53, 68, 72, 140, 159, 212, 284
Badness: 0.000798
13-limit
Commas: 325/324, 385/384, 625/62413 and 15 limit minimax tuning
[|1 0 0 0 0 0>, |4/3 0 0 -2/9 -2/9 4/9>,
|19/9 0 0 -5/27 -5/27 10/27>,
|28/9 0 0 13/27 -14/27 1/27>,
|28/9 0 0 -14/27 13/27 1/27>,
|28/9 0 0 -14/27 -14/27 28/27>]
Eigenmonzos: 2, 13/11, 14/11
Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|]
Generators: 2, 6/5, 7
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299
Badness: 0.000680
Scales: enlil19_13
Enki
Commas: 3025/3024, 4375/4356Minimax tuning
[|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>,
|-2/13 0 5/13 -5/13 10/13>,
|-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>]
Eigenmonzos: 2, 11/8, 7/5
Map: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|]
Generators: 2, 6/5, 66/25
Edos: 15, 49, 57, 72, 87, 159, 193, 231, 265, 280, 337, 352, 439
Badness: 0.00109
13-limit
Commas: 325/324, 364/363, 625/62413 and 15 limit
[|1 0 0 0 0 0>, |2/3 0 -2/3 0 0 2/3>,
|14/9 0 -5/9 0 0 5/9>, |0 0 0 1 0 0>,
|13/9 0 -4/9 1/2 0 4/9>,
|14/9 0 -14/9 0 0 14/9>]
Eigenmonzos: 2, 8/7 13/10
Map: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|]
Generators: 2, 6/5, 66/25
Edos: 15, 72, 87, 159, 193, 280, 439
Badness: 0.000874
Isimud
Commas: 4125/4096, 8019/8000Map: [<1 0 1 0 9|, <0 6 5 0 -21|, <0 0 0 1 0|]
EDOs: 19, 53, 72, 197e, 269ce, 341ce, 375cde, 447cde, 519bcde
Badness: 0.003690
13-limit
Commas: 325/324, 625/624, 1287/1280Map: [<1 0 1 0 9 0|, <0 6 5 0 -21 14|, <0 0 0 1 0 0|]
EDOs: 19, 53, 72, 178def, 197ef, 231ef, 250def, 303cdef
Badness: 0.002273